What should Omega Watch do from battery replacement to circuit corrosion?

I suggest you go to specialty store, where you'd better sell them. Any maintenance is a commercial activity, and they must make more money, including after-sales service. Just say that there is something wrong with the watch you sell, and they will help you repair it, but they will not admit that there is something wrong with the watch. You said you wanted to repair it from the beginning, so they didn't have any pressure to ask you to pay more.